measurement blackline masters

Find each perimeter. Then find each area in square units.

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Discovering Math, Measurement, Basic Measures...or, In, Around, and About

LEVEL

1

Name Date

BASIC MEASURES

Perimeter is the distance around a shape.

Add the lengths to find the perimeter: 4 � 2 � 4 � 2 � 12

The perimeter is 12 units.

Area is the number of square units needed to cover a shape.

Count the total number of squares in therectangle above to find its area.

Volume is the number of cubes it takes tofill a space.

Count the number of cubes to find the volume of the figure.

8 squares cover the rectangle.

The area is 8 square units.

There are 16 cubes.The volume is 16 cubic units.

1.

[10 units; 6 square units]

2.


3.


Find each volume in cubic units.

4.

[6 cubic units]

5.

[8 cubic units]

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BASIC MEASURES


Add the lengths to find the perimeter: 3 units � 4 units � 5 units � 12 units


Area is the number of square units needed to cover a shape exactly.

12 squares cover the rectangle.The area is 12 square units.

Volume is the number of unit cubes it takes to fill a space exactly.

There are 16 unit cubes.The volume is 16 cubic units.

Find each perimeter.

1.

[21 units]

2.

[22 units]

3.

[24 units]

Find the area. Find the volume.

4.

[12 square units]

5.

[12 cubic units]

LEVEL

2

3 units

4 units5 units

7 units 7 units

7 units

3 units

8 units 6 units

6 units

6 units6 units

BASIC MEASURES

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LEVEL

3


Add the lengths of all the sides to find theperimeter: 12 cm � 12 cm � 10 cm � 34 cm

The perimeter is 34 centimeters.

Area is the number of square units neededto cover a shape. Multiply the length by thewidth to find the area of a rectangle.

A � 9 ft � 6 ft � 54 sq ft

The area of the rectangle is 54 square feet.

Volume is the number of cubic units ittakes to fill a space. Multiply the length bythe width by the height to find the volumeof a box.

V � 6 in. � 3 in. � 5 in. � 90 cu. in.

The volume of the box is 90 cubic inches.

Find the perimeter. Find the area. Find the volume.

1.

[100 in.]

2.

[28 sq ft]

3.

[36 cu in.]

12 cm 12 cm

10 cm

7 ft

4 ft9 in.

2 in.2 in.

9 ft

6 ft

5 in.

6 in.

3 in.

36 in.

14 in.

Which tool was used to make each measurement? Write ruler, measuring cup, thermometer, or scale.

Different tools are used to measure different things. For example:

Choose the best tool to measure each item. Write ruler, measuring cup, thermometer, or scale.

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Discovering Math, Measurement, Tools for Measurement...or, It’s Instrumental

LEVEL

1

Name Date

TOOLS FOR MEASUREMENT

Length

Rulers

Temperature

Thermometers

Volume

Measuring cups

Weight

Scales

1. the temperature outside

[thermometer]

3. the weight of a bag of apples

[scale]

2. the length of a ribbon

[ruler]

4. the amount of milk in a container

[measuring cup]

5. The paper is 8 inches long.

[ruler]

7. The water freezes at 32°F.

[thermometer]

6. The cook uses 1 cup of juice.

[measuring cup]

8. The cat weighs 10 pounds.

[scale]

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Choose the best tool to measure each item. Write ruler, tape measure, measuring cup, measuring spoon, protractor, or scale.

Length

Rulers, tape measures

Angle Measure

Protractors

Volume

Measuring cups, measuring spoons

Weight or Mass

Scales, balances


LEVEL

2

1. the width of a door

[ruler or tape measure]

2. the angle of a corner

[protractor]

Which tool was used to make each measurement? Write ruler, measuring cup, protractor, or scale.

3. The cook uses �12� cup of milk.

[measuring cup]

5. The angle has a measure of 60°.

[protractor]

4. The book weighs 10 ounces.

[scale]

6. The model is 6 inches long.

[ruler]


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LEVEL

3

The appropriate tool should be used to make a measurement. For example:

Length: rulers, yardsticks, tape measures, meter sticksUse rulers for shorter lengths and yardsticks or tape measures for longer lengths.Units of length include inches, feet, yards, centimeters, and meters.

Volume: measuring spoons, measuring cups, gallon containersUnits of volume include cups, gallons, and liters.

AngleMeasure: protractors

An angle opening is measured in degrees.

Weightor Mass: scales, balances

Units of weight include ounces or pounds. Units of mass include grams or kilograms.

Choose the best tool to measure each item. Write ruler, yardstick, tape measure, meter stick, gallon container, measuring cup, measuringspoon, protractor, scale, or balance.

1. an angle of 30°

[protractor]

2. the length of a caterpillar

[ruler]

What does each measurement measure? Write length, volume, angle measure, mass, or weight. Then write the tool used to make eachmeasurement. Write ruler, measuring cup, protractor, scale, or balance.

3. Rita bought 3 pounds of apples.

[weight]

[scale]

4. The pitcher holds 1 liter of water.

[volume]

[measuring cup]

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Discovering Math, Measurement, Sizes of Standard Units...or, It’s the One

Name Date

SIZES OF STANDARD UNITS

1. 2 lb � oz [32]

4. 2 pt � c [4]

7. 10 ft � in. [120]

10. 8 pt � qt [4]

2. 3 qt � pt [6]

5. 4 gal � qt [16]

8. 6 c � pt [3]

11. 8 c � qt [2]

3. 4 ft � in. [48]

6. 5 lb � oz [80]

9. 8 qt � gal [2]

12. 5 qt � c [20]

CHALLENGE

A melon weighs 2 pounds 5 ounces. Another melon weighs 2 pounds 8ounces. How many ounces do the two melons weigh in all?

[77 oz]

LEVEL

1

Multiply by smaller units per larger unit to convert from a larger unit to a smaller unit. The measurement becomes a greater number of smaller units.Divide by smaller units per larger units to convert from a smaller unit to a larger unit. The measurement becomes a lesser number of larger units

Write each missing number.

Length

12 inches (in.) � 1 foot (ft)

2 ft � ? in. 2 ft � 12

�inft.

�� 24 in.

2 ft � 24 in.

Weight

16 ounces (oz) � 1 pound (lb)

3 lb � ? oz3 lb � 16

�olbz�

� 48 oz

3 lb � 48 oz

Liquid Volume

1 pint (pt) � 2 cups (c) 12 qt � ? gal1 quart (qt) � 4 cups (c) 12 qt � 4

�gqatl

�� 3 gal

1 quart (qt) � 2 pints (pt)12 qt � 3 gal

1 gallon (gal) � 4 qt

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LEVEL

2


1. 48 in. � ft [4]

4. 8 lb � oz [128]

7. 12 qt � gal [3]

2. 32 oz � lb [2]

5. 8 ft � in. [96]

8. 120 in. � ft [10]

3. 6 gal � qt [24]

6. 5 qt � pt [10]

9. 80 oz � lb [5]

10. 2 lb 5 oz � oz [37]

12. 6 qt 1 pt � pt [13]

11. 4 ft 9 in. � in. [57]

13. 3 gal 2 qt � qt [14]

Use equivalent measures to convert standard units.To change from a larger unit to a smaller unit, multiply by smaller units per larger unit.The measurement becomes a greater number of smaller units. To change from a smaller unit to a larger unit, divide by smaller units per larger unit. The measurement becomes a lesser number of larger units.

Length12 inches (in.) � 1 foot (ft)

6 ft 5 in. � ? in. Think: A foot is a larger unit than an inch.

Multiply to convert 6 ft to inches: 6 ft � 12�inft.

�� 72 in.

Add to find the total: 6 ft 5 in. � 72 in. � 5 in. � 77 in.

Weight16 ounces (oz) � 1 pound (lb)

48 oz � ? lb Think: An ounce is a smaller unit than a pound.There are many ounces in a pound, thus fewer pounds than ounces in the same weight.

Divide: 48 oz � 16�olbz�

� 3 lb

48 oz � 3 lb

Liquid Volume1 pint (pt) � 2 cups (c) 12 pt � ? qt1 quart (qt) � 4 cups (c) 12 pt � 2 �

pqtt

� � 6 qt1 quart (qt) � 2 pints (pt)

12 pt � 6 qt1 gallon (gal) � 4 qt



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Use equivalent measures to convert standard units.Multiply by smaller units per larger unit to convert from a larger unit to a smaller unit. The measurrement becomes a greater number of smaller units.Divide by smaller units per larger unit to convert from a smaller unit to a larger unit. The measurement becomes a lesser number of larger units.



3 ft � 1 yard (yd)

40 in. � ? ft 40 in. � 12

�inft.

�� 3 R4 ft

40 in. � 3 ft 4 in.


3 �12� lb � ? oz

3 �12� lb � 16

�olbz�

� �72� lb � 16

�olbz�

= 56 oz

3 �12� lb � 56 oz

1. 2 �12� ft � in. [30]

4. 3 �14� ft � in. [39]

2. 1 �34� lb � oz

5. 2 �34� qt � c [11]

3. 2 gal � c [32]

6. 72 in. � yd [2]

Liquid Volume1 pint (pt) � 2 cups (c) Sometimes, more than one 1 quart (qt) � 4 cups (c) conversion is needed.1 quart (qt) � 2 pints (pt) 3 gal � ? cups1 gallon (gal) � 4 qt 3 gal � 3 gal � 4

�gqatl

�� 12 qt

3 gal � 12 qt � 4�qct

�� 48 c

[28]

LEVEL

3

7. 35 in. � ft in. [2] [11]

9. 60 oz � lb oz [3] [12]

11. 20 ft � yd ft [6] [2]

13. 62 in. � ft in. [5] [2]

8. 14 qt � gal qt [3] [2]

10. 57 in. � ft in. [4] [9]

12. 85 oz � lb oz [5] [5]

14. 15 c � qt c[3] [3]

Figures with the same perimeter can have different areas.

Find the perimeter and area of each figure. Which figure in each group has the greatest area?

1.

Perimeter:

Area:

[The square has the greatest area.]

2.

Perimeter:

Area:


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Discovering Math, Measurement, Areas and Perimeters...or, In and Around

LEVEL

1

Name Date

AREAS AND PERIMETERS

Add the side lengths to find the perimeter:

P = 6 + 2 + 6 + 2 = 16

Perimeter: 16 in.

Multiply the length by the width to find the area:

A = 6 � 2 = 12

Area: 12 square inches


P = 5 + 3 + 5 + 3 = 16

Perimeter: 16 in.


A = 5 � 3 = 15


6 in.

2 in.

5 in.

3 in.

10 cm2 cm

8 cm

4 cm

6 cm

6 cm

4 ft

12 ft 10 ft

6 ft

8 ft

8 ft

[24 cm]

[20 sq cm]

[32 ft] [32 ft] [32 ft]

[48 sq ft] [60 sq ft] [64 sq ft]

[32 sq cm] [36 sq cm]

[24 cm] [24 cm]

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LEVEL

2



Perimeter of Rectangle A Perimeter of Rectangle B Perimeter of Square CP = 12 + 4 + 12 + 4 = 32 P = 10 + 6 + 10 + 6 = 32 P = 8 + 8 + 8 + 8 = 32Perimeter = 32 cm Perimeter = 32 cm Perimeter = 32 cm

Area of Rectangle A Area of Rectangle B Area of Square CA = l � w = 12 � 4 = 48 A = l � w = 10 � 6 = 60 A = l � w = 8 � 8 = 64Area = 48 sq cm Area = 60 sq cm Area = 64 sq cm

As the sides of the rectangles get closer in length, the area increases but the perimeter does not change.

The perimeters are all the same for the rectangles within a group.Predict the figure in each group that will have the greatest area. Then find the perimeter and area of each figure.

1.

Prediction: [Figure C has the greatest area.]

Perimeter: A: B: C: [24 in.][24 in.][24 in.]

Area: A: B: C: [20 sq in.][32 sq in.][36 sq in.]

12 cm

4 cm

Rectangle A

10 in.

2 in. A

8 in.

4 in. B

6 in.

6 in. C

6 cm

10 cm

Rectangle B

8 cm

8 cm

Square C


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When the lengths of sides of a figure are doubled, keeping the figure the same shape, theperimeter is doubled, but the area is increased by 4 times.

Perimeter of Rectangle A Perimeter of Rectangle BP = 6 + 4 + 6 + 4 = 20 P = 12 + 8 + 12 + 8 = 40Perimeter = 20 cm Perimeter = 40 cm

As the lengths of the sides are doubled, the perimeter doubles.

Area of Rectangle A Area of Rectangle BA = l � w = 6 � 4 = 24 A = l � w = 12 � 8 = 96Area = 24 sq cm Area = 96 sq cm

As the lengths of the sides are doubled, the area is multiplied by 4.

Find the perimeter and area of each figure. Then double the length and width of each figure.Predict the new perimeter and area. Then check the new perimeter and area.

LEVEL

3

6 cm

4 cm

Rectangle A

8 cm

12 cm

Rectangle B

1.

P = [16 ft]

A = [15 sq ft]

[32 ft]

[60 sq ft]

2.

P = [26 in.]

A = [42 sq in.]

[52 in.]

[168 sq in.]

3.

P = [28 m]

A = [45 sq m]

3 ft

5 ft

6 in.

7 in.

5 m

9 m

[180 sq m]

[56 m]

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Discovering Math, Measurement, Variability in Measurement...or, Close Encounters

LEVEL

1

Name Date

VARIABILITY IN MEASUREMENT

Measurement in inches may be to the nearest inch, �12�-inch, or �

14�-inch.

To make an accurate measurement, align the left edge of theitem being measured with the left edge or “0” mark on the ruler.

To the nearest inch, the paper clip is 1 inch long.To the nearest �

12�-inch, the paper clip is 1�

12� inches long.

To the nearest �14�-inch, the paper clip is 1�

14� inches long.

The measurement of 1�14� inches is the most accurate since it

uses the smallest unit to make the measurement, so it’s closest to the true value.

Which measurement is the most accurate? Explain why.

1.

[1�12� in. is more accurate since the left end of the straw is aligned with the left end of the ruler.

The other straw is not aligned at the end, so the measurement differs more from the true length.]

2.

[2�34� in. is more accurate since it is within a smaller unit of the true length, so the

measurement is closer to the true value. The left ends of the pencils are both aligned

with the left end of the rulers.]

1 in.12 1 in.3

4

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LEVEL

2


Using a customary ruler marked in inches and eighths of inches, you can measure reliablyto the nearest �

18�-inch. The smaller the unit of measurement, the more precise the measurement

can be. If the ruler is accurate, smaller divisions allow reliable measurement closer to thetrue value, which are therefore more accurate measurements.

To make an accurate measurement, align the left edge of the item being measured with the left edge or “0” mark on the ruler.

To the nearest �12�-inch, the string is 1�

12� inches long.


34� inches long.


58� inches long.

The measurement of 1�58� inches is the most precise, to the nearest �

18� –inch, and the most

accurate since it uses the smallest unit, so it’s closest to the true value.


1.

[2�18� in. is more accurate since the left end of the straw is aligned with the left end of the ruler,

so the recorded length is closer to the true value. The other straw is not aligned at the end.]

2. A scale in the produce section of a grocery store measures weight inpounds, with no smaller intervals. When Jill puts a melon on the scale, it shows the weight to the nearest marking as 2 pounds. When the clerkputs the same melon on a scale at the register, the measurement is 2pounds 5 ounces. Both scales read “0” when nothing is on the scales.Assuming both scales are accurate, which measurement is more accurate?

[The scale at the register is more accurate since it shows smaller units, so its

measurement is closer to the true value.]

2 in.18 2 in.5

8


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LEVEL

3

The precision and accuracy of a measurement may depend upon the units of measurement used. A length measured to the nearest �

18�-inch

is more precise than a length measured to the nearest inch, since �18�-inch is a smaller unit. If the ruler is accurate, the measurement will usually also be more accurate, because it will be closer to the true value, within �

18� inch

rather than only within a greater interval.

The accuracy of a measurement may depend upon the tool used to measure. A scale that is set at “0” when it is empty is usually more accurate than a scale that is not set at “0.”


1. Lonnie measures a string using a ruler. He says the string is 4�136� inches

long. Randy measures the same string using a different ruler. He saysthe string is 4�

14� inches long. Both friends align the end of the string with

the left ends of their rulers and measure to the nearest marking. Whosemeasurement is more accurate?

[Lonnie’s because he uses the smaller unit, so his measurement is therefore closer to the true value,

to the closest �116� inch rather than only to the closest �

14� inch.]

CHALLENGE

Which measurement is more accurate? Explain.

[1�12� in., because the reported length happens to be closer to the true value.]

With which ruler could you generally make measurements precise to within acloser interval?

[The second, because the intervals are smaller, so you could repeat

measurements to a smaller interval reliably.]

1 in.12 1 in.1

4

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Discovering Math, Measurement, Estimation Strategy... or, How About It?

LEVEL

1

Name Date

ESTIMATION STRATEGIES

You can estimate to help you make decisions about money.

Kendra has $8.00 to spend at the book store. She wants to buy a book that costs $4.95 and a magazine that costs $3.19. Does she have enough money to buy both items?

Round each amount to estimate the total.

The book costs about $5.00.The magazine costs about $3.20.$5.00 � $3.20 � $8.20

Compare the total with the amount she has.

$8.20 � $8.00

$8.20 is more than the amount Kendra has. She does not have enough money to buy both items.

Use an estimate to solve each problem.

1. Enrico has $10.00. He wants to buy some watercolors that cost $7.49and a paint brush that costs $1.99. Does he have enough money to buyboth items? Explain.

[Yes: $7.50 � $2.00 � $9.50 and $9.50 � $10.00]

2. Lourdes has $3.00. She wants to buy 4 different markers that cost$0.69 each. Does she have enough money to buy all the markers?Explain.

[Yes. Each marker costs about $0.70 and $0.70 � 4 � $2.80 and $2.80 � $3.00.]

3. Ryan has $15.00. He wants to buy 2 magazines that cost $4.25 eachand a guidebook that costs $8.79. Does he have enough money to buyall the items? Explain.

[No. $4.00 � $4.00 � $8.00, $8.00 � $9.00 � $17.00, and $17.00 � $15.00.]

[Estimates may vary. Accept reasonable estimates. Sample estimates are given.]

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LEVEL

2



Corey is able to save $3.00 each week. He wants to save the money to buy a new game. The game costs $29.95. How many weeks will Corey have to save money before he has enough to buy the game?

Savings each week: $3.00 Cost of game: about $30.00

Divide to find about how many weeks Corey will have to save.

Corey will have to save money for about 10 weeks to buy the game.


1. Lara can save $4.00 each month. She wants to save the money to buya new pair of skates that cost $38.50. How many months will Lara haveto save money before she has enough to buy the skates?

[about 10 months]

2. Jason plans to save $3.25 each week to buy a birthday gift for hismother. He wants to buy her a vase that costs $45.00. How manyweeks should Jason plan on saving money to have enough to buy thevase?

[about 15 weeks]

3. Eva is saving $2.25 each week to buy a new book that will cost$13.95. How many weeks will Eva have to save money so that she willhave enough to buy the book?

[about 7 weeks]

103�3�0��3�0�

0



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LEVEL

3



Paula and Greg want to earn $2,000 to redecorate a room. Paula works Saturdays at a banquet hall. She earns $75 each time she works. Greg works afternoons at a market. He earns $32 each afternoon he works. Paula will work every Saturday until she earns $800. Greg will work 3 afternoons a week until he earns $1200. How many weeks will each person have to work to meet their goals?

Estimate the number of weeks Paula needs to work.$800 � $80 � 10 Since $75 � $80, adjust the estimate: add 1 more week.

Paula needs to work about 11 weeks.

Estimate the number of weeks Greg needs to work.He earns about $30 � 3, or about $90, each week. $1,200 � $90 ≈ $1,200 � $100 � 12 Since $90 � $100, adjust the estimate: add 1 more week.

Greg needs to work about 13 weeks.


1. Marc wants to earn $350 to buy a new printer. He does yard workevery weekend and earns $7.50 each hour he works. He works about 8hours every weekend. How many weekends will Marc have to work tomeet his goal?

[about 6 weekends]

2. Rebecca wants to earn $700 to buy a new computer. She works in acrafts shop twice a week. She works 4 hours each time she works andearns $8.10 each hour she works. How many weeks will Rebecca haveto work to meet her goal?

[about 11 weeks]

Inches, feet, yards, and miles are customary units of length.Centimeters, meters, and kilometers are metric units of length.

Different units are used to measure different lengths.

Choose the unit you would use to measure each length. Write inches, feet, or miles.

Choose the unit you would use to measure each length. Write centimeters, meters, or kilometers.

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Discovering Math, Measurement, Selecting Units...or, Sizing It Up

LEVEL

1

Name Date

SELECTING UNITS

Use inches or centimetersto measure the length of apencil.

Use feet, yards, or metersto measure the height of abuilding.

Use miles or kilometers tomeasure the distancebetween cities.

1. length of a spoon

[inches]

3. height of a giraffe

[feet]

5. length of a crayon

[inches]

2. distance a horse walks in 2 hours

[miles]

4. length of a whale

[feet]

6. distance from Orlando to Miami

[miles]

CHALLENGEYou can use cups or gallons to measure capacity. Which would you use to measure the amount of water needed to fill a bath tub?

[gallons]

7. length of a bus

[meters]

9. distance from Paris to Madrid

[kilometers]

8. height of a home aquarium

[centimeters]

10. height of a flagpole

[meters]

CHALLENGE

You can use milliliters or liters to measure volume. Which would you use to measure the amount of juice in a glass of orange juice?

[milliliters]

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LEVEL

2

SELECTING UNITS

Different units of measurement are used to measure different lengths:length of a ladybug: use millimeters.height of a cereal box: use inches or centimeters.length of a football field: use feet, yards, or meters.distance between cities: use miles or kilometers.

Choose the customary unit you would use to measure each length.

Choose the metric unit you would use to measure each length.

Customary Units of Lengthinches, feet, yards, miles

Metric Units of Lengthmillimeters, centimeters, meters, kilometers

1. length of a fork

[inches]

3. height of a lion

[inches or feet]

5. height of a tree

[feet or yards]

2. distance a cyclist rides in 3 hours

[miles]


[feet or yards]

6. distance from Dallas to Denver

[miles]

7. length of an ant

[millimeters]

9. distance from Rome to Berlin

[kilometers]

8. height of a dog

[centimeters]

10. height of a skyscraper

[meters]

Choose the metric unit you would use to measure.

SELECTING UNITS

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LEVEL

3

Use smaller units to measure lesser lengths and larger units to measure greater lengths. Inches are smaller units than feet. Use inches to measure the width of a car window, but use feet to measure the length of a car.

Use smaller units to measure lesser volumes or capacities and larger units to measure greater volumes or capacities.Gallons are larger units than quarts. Use gallons to measure the amount of gas needed tofuel a car, but use quarts to measure the oil a car uses.

Choose the customary unit you would use to measure each.

Customary Units of Measurement

Length: inches, feet, yards, miles

Volume or Capacity: cups, pints, quarts, gallons

Metric Units of Measurement

Length: millimeters, centimeters, meters, kilometers

Volume or Capacity: milliliters, liters

1. length of an eraser

[inches]

3. milk in a bowl of cereal

[cups]

2. length of an airplane

[feet or yards]

4. distance a runner runs in 2 hours

[miles]

5. water in a teaspoon

[milliliters]

7. water to fill a washing machine

[liters]

6. length of a marathon

[kilometers]

8. length of a ladybug

[millimeters]

Find each perimeter. Then find each area in square units.

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LEVEL

1

Name Date

BASIC MEASURES


Add the lengths to find the perimeter: 4 � 2 � 4 � 2 � 12


Area is the number of square units needed to cover a shape.

Count the total number of squares in therectangle above to find its area.

Volume is the number of cubes it takes tofill a space.

Count the number of cubes to find the volume of the figure.

8 squares cover the rectangle.

The area is 8 square units.

There are 16 cubes.The volume is 16 cubic units.

1.


2.


3.


Find each volume in cubic units.

4.

[6 cubic units]

5.

[8 cubic units]

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BASIC MEASURES


Add the lengths to find the perimeter: 3 units � 4 units � 5 units � 12 units


Area is the number of square units needed to cover a shape exactly.

12 squares cover the rectangle.The area is 12 square units.

Volume is the number of unit cubes it takes to fill a space exactly.

There are 16 unit cubes.The volume is 16 cubic units.

Find each perimeter.

1.

[21 units]

2.

[22 units]

3.

[24 units]

Find the area. Find the volume.

4.

[12 square units]

5.

[12 cubic units]

LEVEL

2

3 units

4 units5 units

7 units 7 units

7 units

3 units

8 units 6 units

6 units

6 units6 units

BASIC MEASURES

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LEVEL

3


Add the lengths of all the sides to find theperimeter: 12 cm � 12 cm � 10 cm � 34 cm

The perimeter is 34 centimeters.

Area is the number of square units neededto cover a shape. Multiply the length by thewidth to find the area of a rectangle.

A � 9 ft � 6 ft � 54 sq ft

The area of the rectangle is 54 square feet.

Volume is the number of cubic units ittakes to fill a space. Multiply the length bythe width by the height to find the volumeof a box.

V � 6 in. � 3 in. � 5 in. � 90 cu. in.

The volume of the box is 90 cubic inches.

Find the perimeter. Find the area. Find the volume.

1.

[100 in.]

2.

[28 sq ft]

3.

[36 cu in.]

12 cm 12 cm

10 cm

7 ft

4 ft9 in.

2 in.2 in.

9 ft

6 ft

5 in.

6 in.

3 in.

36 in.

14 in.

Which tool was used to make each measurement? Write ruler, measuring cup, thermometer, or scale.


Choose the best tool to measure each item. Write ruler, measuring cup, thermometer, or scale.

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LEVEL

1

Name Date


Length

Rulers

Temperature

Thermometers

Volume

Measuring cups

Weight

Scales

1. the temperature outside

[thermometer]

3. the weight of a bag of apples

[scale]

2. the length of a ribbon

[ruler]

4. the amount of milk in a container

[measuring cup]

5. The paper is 8 inches long.

[ruler]

7. The water freezes at 32°F.

[thermometer]

6. The cook uses 1 cup of juice.

[measuring cup]

8. The cat weighs 10 pounds.

[scale]

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Choose the best tool to measure each item. Write ruler, tape measure, measuring cup, measuring spoon, protractor, or scale.

Length

Rulers, tape measures

Angle Measure

Protractors

Volume

Measuring cups, measuring spoons

Weight or Mass

Scales, balances


LEVEL

2

1. the width of a door

[ruler or tape measure]

2. the angle of a corner

[protractor]

Which tool was used to make each measurement? Write ruler, measuring cup, protractor, or scale.

3. The cook uses �12� cup of milk.

[measuring cup]

5. The angle has a measure of 60°.

[protractor]

4. The book weighs 10 ounces.

[scale]

6. The model is 6 inches long.

[ruler]


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LEVEL

3

The appropriate tool should be used to make a measurement. For example:

Length: rulers, yardsticks, tape measures, meter sticksUse rulers for shorter lengths and yardsticks or tape measures for longer lengths.Units of length include inches, feet, yards, centimeters, and meters.

Volume: measuring spoons, measuring cups, gallon containersUnits of volume include cups, gallons, and liters.

AngleMeasure: protractors

An angle opening is measured in degrees.

Weightor Mass: scales, balances

Units of weight include ounces or pounds. Units of mass include grams or kilograms.

Choose the best tool to measure each item. Write ruler, yardstick, tape measure, meter stick, gallon container, measuring cup, measuringspoon, protractor, scale, or balance.

1. an angle of 30°

[protractor]

2. the length of a caterpillar

[ruler]

What does each measurement measure? Write length, volume, angle measure, mass, or weight. Then write the tool used to make eachmeasurement. Write ruler, measuring cup, protractor, scale, or balance.

3. Rita bought 3 pounds of apples.

[weight]

[scale]

4. The pitcher holds 1 liter of water.

[volume]

[measuring cup]

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1. 2 lb � oz [32]

4. 2 pt � c [4]

7. 10 ft � in. [120]

10. 8 pt � qt [4]

2. 3 qt � pt [6]

5. 4 gal � qt [16]

8. 6 c � pt [3]

11. 8 c � qt [2]

3. 4 ft � in. [48]

6. 5 lb � oz [80]

9. 8 qt � gal [2]

12. 5 qt � c [20]

CHALLENGE

A melon weighs 2 pounds 5 ounces. Another melon weighs 2 pounds 8ounces. How many ounces do the two melons weigh in all?

[77 oz]

LEVEL

1

Multiply by smaller units per larger unit to convert from a larger unit to a smaller unit. The measurement becomes a greater number of smaller units.Divide by smaller units per larger units to convert from a smaller unit to a larger unit. The measurement becomes a lesser number of larger units


Length

12 inches (in.) � 1 foot (ft)

2 ft � ? in. 2 ft � 12

�inft.

�� 24 in.

2 ft � 24 in.

Weight

16 ounces (oz) � 1 pound (lb)

3 lb � ? oz3 lb � 16

�olbz�

� 48 oz

3 lb � 48 oz

Liquid Volume

1 pint (pt) � 2 cups (c) 12 qt � ? gal1 quart (qt) � 4 cups (c) 12 qt � 4

�gqatl

�� 3 gal

1 quart (qt) � 2 pints (pt)12 qt � 3 gal

1 gallon (gal) � 4 qt

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LEVEL

2


1. 48 in. � ft [4]

4. 8 lb � oz [128]

7. 12 qt � gal [3]

2. 32 oz � lb [2]

5. 8 ft � in. [96]

8. 120 in. � ft [10]

3. 6 gal � qt [24]

6. 5 qt � pt [10]

9. 80 oz � lb [5]

10. 2 lb 5 oz � oz [37]

12. 6 qt 1 pt � pt [13]

11. 4 ft 9 in. � in. [57]

13. 3 gal 2 qt � qt [14]

Use equivalent measures to convert standard units.To change from a larger unit to a smaller unit, multiply by smaller units per larger unit.The measurement becomes a greater number of smaller units. To change from a smaller unit to a larger unit, divide by smaller units per larger unit. The measurement becomes a lesser number of larger units.


6 ft 5 in. � ? in. Think: A foot is a larger unit than an inch.

Multiply to convert 6 ft to inches: 6 ft � 12�inft.

�� 72 in.

Add to find the total: 6 ft 5 in. � 72 in. � 5 in. � 77 in.


48 oz � ? lb Think: An ounce is a smaller unit than a pound.There are many ounces in a pound, thus fewer pounds than ounces in the same weight.

Divide: 48 oz � 16�olbz�

� 3 lb

48 oz � 3 lb

Liquid Volume1 pint (pt) � 2 cups (c) 12 pt � ? qt1 quart (qt) � 4 cups (c) 12 pt � 2 �

pqtt

� � 6 qt1 quart (qt) � 2 pints (pt)

12 pt � 6 qt1 gallon (gal) � 4 qt



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Use equivalent measures to convert standard units.Multiply by smaller units per larger unit to convert from a larger unit to a smaller unit. The measurrement becomes a greater number of smaller units.Divide by smaller units per larger unit to convert from a smaller unit to a larger unit. The measurement becomes a lesser number of larger units.



3 ft � 1 yard (yd)

40 in. � ? ft 40 in. � 12

�inft.

�� 3 R4 ft

40 in. � 3 ft 4 in.


3 �12� lb � ? oz

3 �12� lb � 16

�olbz�

� �72� lb � 16

�olbz�

= 56 oz

3 �12� lb � 56 oz

1. 2 �12� ft � in. [30]

4. 3 �14� ft � in. [39]

2. 1 �34� lb � oz

5. 2 �34� qt � c [11]

3. 2 gal � c [32]

6. 72 in. � yd [2]

Liquid Volume1 pint (pt) � 2 cups (c) Sometimes, more than one 1 quart (qt) � 4 cups (c) conversion is needed.1 quart (qt) � 2 pints (pt) 3 gal � ? cups1 gallon (gal) � 4 qt 3 gal � 3 gal � 4

�gqatl

�� 12 qt

3 gal � 12 qt � 4�qct

�� 48 c

[28]

LEVEL

3

7. 35 in. � ft in. [2] [11]

9. 60 oz � lb oz [3] [12]

11. 20 ft � yd ft [6] [2]

13. 62 in. � ft in. [5] [2]

8. 14 qt � gal qt [3] [2]

10. 57 in. � ft in. [4] [9]

12. 85 oz � lb oz [5] [5]

14. 15 c � qt c[3] [3]


Find the perimeter and area of each figure. Which figure in each group has the greatest area?

1.

Perimeter:

Area:


2.

Perimeter:

Area:


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1

Name Date



P = 6 + 2 + 6 + 2 = 16

Perimeter: 16 in.


A = 6 � 2 = 12



P = 5 + 3 + 5 + 3 = 16

Perimeter: 16 in.


A = 5 � 3 = 15


6 in.

2 in.

5 in.

3 in.

10 cm2 cm

8 cm

4 cm

6 cm

6 cm

4 ft

12 ft 10 ft

6 ft

8 ft

8 ft

[24 cm]

[20 sq cm]

[32 ft] [32 ft] [32 ft]

[48 sq ft] [60 sq ft] [64 sq ft]

[32 sq cm] [36 sq cm]

[24 cm] [24 cm]

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LEVEL

2



Perimeter of Rectangle A Perimeter of Rectangle B Perimeter of Square CP = 12 + 4 + 12 + 4 = 32 P = 10 + 6 + 10 + 6 = 32 P = 8 + 8 + 8 + 8 = 32Perimeter = 32 cm Perimeter = 32 cm Perimeter = 32 cm

Area of Rectangle A Area of Rectangle B Area of Square CA = l � w = 12 � 4 = 48 A = l � w = 10 � 6 = 60 A = l � w = 8 � 8 = 64Area = 48 sq cm Area = 60 sq cm Area = 64 sq cm

As the sides of the rectangles get closer in length, the area increases but the perimeter does not change.

The perimeters are all the same for the rectangles within a group.Predict the figure in each group that will have the greatest area. Then find the perimeter and area of each figure.

1.

Prediction: [Figure C has the greatest area.]

Perimeter: A: B: C: [24 in.][24 in.][24 in.]

Area: A: B: C: [20 sq in.][32 sq in.][36 sq in.]

12 cm

4 cm

Rectangle A

10 in.

2 in. A

8 in.

4 in. B

6 in.

6 in. C

6 cm

10 cm

Rectangle B

8 cm

8 cm

Square C


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When the lengths of sides of a figure are doubled, keeping the figure the same shape, theperimeter is doubled, but the area is increased by 4 times.

Perimeter of Rectangle A Perimeter of Rectangle BP = 6 + 4 + 6 + 4 = 20 P = 12 + 8 + 12 + 8 = 40Perimeter = 20 cm Perimeter = 40 cm

As the lengths of the sides are doubled, the perimeter doubles.

Area of Rectangle A Area of Rectangle BA = l � w = 6 � 4 = 24 A = l � w = 12 � 8 = 96Area = 24 sq cm Area = 96 sq cm

As the lengths of the sides are doubled, the area is multiplied by 4.

Find the perimeter and area of each figure. Then double the length and width of each figure.Predict the new perimeter and area. Then check the new perimeter and area.

LEVEL

3

6 cm

4 cm

Rectangle A

8 cm

12 cm

Rectangle B

1.

P = [16 ft]

A = [15 sq ft]

[32 ft]

[60 sq ft]

2.

P = [26 in.]

A = [42 sq in.]

[52 in.]

[168 sq in.]

3.

P = [28 m]

A = [45 sq m]

3 ft

5 ft

6 in.

7 in.

5 m

9 m

[180 sq m]

[56 m]

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1

Name Date


Measurement in inches may be to the nearest inch, �12�-inch, or �

14�-inch.

To make an accurate measurement, align the left edge of theitem being measured with the left edge or “0” mark on the ruler.

To the nearest inch, the paper clip is 1 inch long.To the nearest �

12�-inch, the paper clip is 1�

12� inches long.

To the nearest �14�-inch, the paper clip is 1�

14� inches long.

The measurement of 1�14� inches is the most accurate since it

uses the smallest unit to make the measurement, so it’s closest to the true value.


1.

[1�12� in. is more accurate since the left end of the straw is aligned with the left end of the ruler.

The other straw is not aligned at the end, so the measurement differs more from the true length.]

2.

[2�34� in. is more accurate since it is within a smaller unit of the true length, so the

measurement is closer to the true value. The left ends of the pencils are both aligned

with the left end of the rulers.]

1 in.12 1 in.3

4

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LEVEL

2


Using a customary ruler marked in inches and eighths of inches, you can measure reliablyto the nearest �

18�-inch. The smaller the unit of measurement, the more precise the measurement

can be. If the ruler is accurate, smaller divisions allow reliable measurement closer to thetrue value, which are therefore more accurate measurements.

To make an accurate measurement, align the left edge of the item being measured with the left edge or “0” mark on the ruler.


12� inches long.


34� inches long.


58� inches long.

The measurement of 1�58� inches is the most precise, to the nearest �

18� –inch, and the most

accurate since it uses the smallest unit, so it’s closest to the true value.


1.

[2�18� in. is more accurate since the left end of the straw is aligned with the left end of the ruler,

so the recorded length is closer to the true value. The other straw is not aligned at the end.]

2. A scale in the produce section of a grocery store measures weight inpounds, with no smaller intervals. When Jill puts a melon on the scale, it shows the weight to the nearest marking as 2 pounds. When the clerkputs the same melon on a scale at the register, the measurement is 2pounds 5 ounces. Both scales read “0” when nothing is on the scales.Assuming both scales are accurate, which measurement is more accurate?

[The scale at the register is more accurate since it shows smaller units, so its

measurement is closer to the true value.]

2 in.18 2 in.5

8


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LEVEL

3

The precision and accuracy of a measurement may depend upon the units of measurement used. A length measured to the nearest �

18�-inch

is more precise than a length measured to the nearest inch, since �18�-inch is a smaller unit. If the ruler is accurate, the measurement will usually also be more accurate, because it will be closer to the true value, within �

18� inch

rather than only within a greater interval.

The accuracy of a measurement may depend upon the tool used to measure. A scale that is set at “0” when it is empty is usually more accurate than a scale that is not set at “0.”


1. Lonnie measures a string using a ruler. He says the string is 4�136� inches

long. Randy measures the same string using a different ruler. He saysthe string is 4�

14� inches long. Both friends align the end of the string with

the left ends of their rulers and measure to the nearest marking. Whosemeasurement is more accurate?

[Lonnie’s because he uses the smaller unit, so his measurement is therefore closer to the true value,

to the closest �116� inch rather than only to the closest �

14� inch.]

CHALLENGE

Which measurement is more accurate? Explain.

[1�12� in., because the reported length happens to be closer to the true value.]

With which ruler could you generally make measurements precise to within acloser interval?

[The second, because the intervals are smaller, so you could repeat

measurements to a smaller interval reliably.]

1 in.12 1 in.1

4

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1

Name Date



Kendra has $8.00 to spend at the book store. She wants to buy a book that costs $4.95 and a magazine that costs $3.19. Does she have enough money to buy both items?

Round each amount to estimate the total.

The book costs about $5.00.The magazine costs about $3.20.$5.00 � $3.20 � $8.20

Compare the total with the amount she has.

$8.20 � $8.00

$8.20 is more than the amount Kendra has. She does not have enough money to buy both items.


1. Enrico has $10.00. He wants to buy some watercolors that cost $7.49and a paint brush that costs $1.99. Does he have enough money to buyboth items? Explain.

[Yes: $7.50 � $2.00 � $9.50 and $9.50 � $10.00]

2. Lourdes has $3.00. She wants to buy 4 different markers that cost$0.69 each. Does she have enough money to buy all the markers?Explain.

[Yes. Each marker costs about $0.70 and $0.70 � 4 � $2.80 and $2.80 � $3.00.]

3. Ryan has $15.00. He wants to buy 2 magazines that cost $4.25 eachand a guidebook that costs $8.79. Does he have enough money to buyall the items? Explain.

[No. $4.00 � $4.00 � $8.00, $8.00 � $9.00 � $17.00, and $17.00 � $15.00.]


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LEVEL

2



Corey is able to save $3.00 each week. He wants to save the money to buy a new game. The game costs $29.95. How many weeks will Corey have to save money before he has enough to buy the game?

Savings each week: $3.00 Cost of game: about $30.00

Divide to find about how many weeks Corey will have to save.

Corey will have to save money for about 10 weeks to buy the game.


1. Lara can save $4.00 each month. She wants to save the money to buya new pair of skates that cost $38.50. How many months will Lara haveto save money before she has enough to buy the skates?

[about 10 months]

2. Jason plans to save $3.25 each week to buy a birthday gift for hismother. He wants to buy her a vase that costs $45.00. How manyweeks should Jason plan on saving money to have enough to buy thevase?

[about 15 weeks]

3. Eva is saving $2.25 each week to buy a new book that will cost$13.95. How many weeks will Eva have to save money so that she willhave enough to buy the book?

[about 7 weeks]

103�3�0��3�0�

0



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LEVEL

3



Paula and Greg want to earn $2,000 to redecorate a room. Paula works Saturdays at a banquet hall. She earns $75 each time she works. Greg works afternoons at a market. He earns $32 each afternoon he works. Paula will work every Saturday until she earns $800. Greg will work 3 afternoons a week until he earns $1200. How many weeks will each person have to work to meet their goals?

Estimate the number of weeks Paula needs to work.$800 � $80 � 10 Since $75 � $80, adjust the estimate: add 1 more week.

Paula needs to work about 11 weeks.

Estimate the number of weeks Greg needs to work.He earns about $30 � 3, or about $90, each week. $1,200 � $90 ≈ $1,200 � $100 � 12 Since $90 � $100, adjust the estimate: add 1 more week.

Greg needs to work about 13 weeks.


1. Marc wants to earn $350 to buy a new printer. He does yard workevery weekend and earns $7.50 each hour he works. He works about 8hours every weekend. How many weekends will Marc have to work tomeet his goal?

[about 6 weekends]

2. Rebecca wants to earn $700 to buy a new computer. She works in acrafts shop twice a week. She works 4 hours each time she works andearns $8.10 each hour she works. How many weeks will Rebecca haveto work to meet her goal?

[about 11 weeks]

Inches, feet, yards, and miles are customary units of length.Centimeters, meters, and kilometers are metric units of length.

Different units are used to measure different lengths.

Choose the unit you would use to measure each length. Write inches, feet, or miles.

Choose the unit you would use to measure each length. Write centimeters, meters, or kilometers.

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LEVEL

1

Name Date

SELECTING UNITS

Use inches or centimetersto measure the length of apencil.

Use feet, yards, or metersto measure the height of abuilding.

Use miles or kilometers tomeasure the distancebetween cities.

1. length of a spoon

[inches]

3. height of a giraffe

[feet]

5. length of a crayon

[inches]

2. distance a horse walks in 2 hours

[miles]

4. length of a whale

[feet]

6. distance from Orlando to Miami

[miles]

CHALLENGEYou can use cups or gallons to measure capacity. Which would you use to measure the amount of water needed to fill a bath tub?

[gallons]

7. length of a bus

[meters]

9. distance from Paris to Madrid

[kilometers]

8. height of a home aquarium

[centimeters]


[meters]

CHALLENGE

You can use milliliters or liters to measure volume. Which would you use to measure the amount of juice in a glass of orange juice?

[milliliters]

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LEVEL

2

SELECTING UNITS

Different units of measurement are used to measure different lengths:length of a ladybug: use millimeters.height of a cereal box: use inches or centimeters.length of a football field: use feet, yards, or meters.distance between cities: use miles or kilometers.

Choose the customary unit you would use to measure each length.

Choose the metric unit you would use to measure each length.

Customary Units of Lengthinches, feet, yards, miles

Metric Units of Lengthmillimeters, centimeters, meters, kilometers

1. length of a fork

[inches]

3. height of a lion

[inches or feet]

5. height of a tree

[feet or yards]

2. distance a cyclist rides in 3 hours

[miles]


[feet or yards]

6. distance from Dallas to Denver

[miles]

7. length of an ant

[millimeters]

9. distance from Rome to Berlin

[kilometers]

8. height of a dog

[centimeters]

10. height of a skyscraper

[meters]

Choose the metric unit you would use to measure.

SELECTING UNITS

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LEVEL

3

Use smaller units to measure lesser lengths and larger units to measure greater lengths. Inches are smaller units than feet. Use inches to measure the width of a car window, but use feet to measure the length of a car.

Use smaller units to measure lesser volumes or capacities and larger units to measure greater volumes or capacities.Gallons are larger units than quarts. Use gallons to measure the amount of gas needed tofuel a car, but use quarts to measure the oil a car uses.

Choose the customary unit you would use to measure each.

Customary Units of Measurement

Length: inches, feet, yards, miles

Volume or Capacity: cups, pints, quarts, gallons

Metric Units of Measurement

Length: millimeters, centimeters, meters, kilometers

Volume or Capacity: milliliters, liters

1. length of an eraser

[inches]

3. milk in a bowl of cereal

[cups]

2. length of an airplane

[feet or yards]

4. distance a runner runs in 2 hours

[miles]

5. water in a teaspoon

[milliliters]

7. water to fill a washing machine

[liters]

6. length of a marathon

[kilometers]

8. length of a ladybug

[millimeters]

measurement blackline masters

Documents

mass include

temperature

liquid volume

selecting

gallon containers

measure lesser

smaller interval

measure greater